    {-# LANGUAGE CPP #-}
    {-# LANGUAGE FlexibleInstances #-}
    {-# LANGUAGE OverloadedStrings #-}
    {-# LANGUAGE TypeSynonymInstances #-}

    --------------------------------------------------------------------------------
    --  See end of this file for licence information.
    --------------------------------------------------------------------------------
    -- |
    --  Module      :  VarBinding
    --  Copyright   :  (c) 2003, Graham Klyne, 2009 Vasili I Galchin,
    --                 2011, 2012, 2014, 2015, 2016 Douglas Burke
    --  License     :  GPL V2
    --
    --  Maintainer  :  Douglas Burke
    --  Stability   :  experimental
    --  Portability :  CPP, FlexibleInstances, OverloadedStrings, TypeSynonymInstances
    --
    --  This module defines functions for representing and manipulating query
    --  binding variable sets.  This is the key data that mediates between
    --  query and back substitution when performing inferences.  A framework
    --  of query variable modifiers is provided that can be used to
    --  implement richer inferences, such as filtering of  query results,
    --  or replacing values based on known relationships.
    --
    --------------------------------------------------------------------------------

    module Swish.VarBinding
        ( VarBinding(..), nullVarBinding
        , boundVars, subBinding, makeVarBinding
        , applyVarBinding, joinVarBindings, addVarBinding
        , VarBindingModify(..), OpenVarBindingModify
        , openVbmName
        , vbmCompatibility, vbmCompose
        , composeSequence, findCompositions, findComposition
        , VarBindingFilter(..)
        , makeVarFilterModify
        , makeVarTestFilter, makeVarCompareFilter
        , varBindingId, nullVarBindingModify
        , varFilterDisjunction, varFilterConjunction
        , varFilterEQ, varFilterNE
        )
    where

    import Swish.Namespace (ScopedName, getScopeLocal)
    import Swish.QName (newLName, getLName)

    import Swish.RDF.Vocabulary (swishName)

    import Swish.Utils.ListHelpers (flist)

    #if (!defined(__GLASGOW_HASKELL__)) || (__GLASGOW_HASKELL__ < 710)
    import Control.Applicative ((<$>), (<*>))
    import Data.Monoid (Monoid(..), mconcat)
    #endif

    import Control.Monad (mplus)

    import Data.Function (on)
    import Data.List (find, intersect, union, (\\), foldl', permutations)
    import Data.Maybe (mapMaybe, fromMaybe, isJust, fromJust, listToMaybe)
    import Data.Ord (comparing)

    import qualified Data.Map as M
    import qualified Data.Set as S

    -- import Prelude

    ------------------------------------------------------------
    --  Query variable bindings
    ------------------------------------------------------------

    -- |VarBinding is the type of an arbitrary variable bindings
    --  value, where the type of the bound values is not specified.
    --
    data VarBinding a b = VarBinding
        { vbMap  :: a -> Maybe b
        , vbEnum :: S.Set (a,b)
        , vbNull :: Bool
        }

    -- | The Eq instance is defined as the set equivalence of the
    --   pairs of variables in the binding.
    --
    instance (Ord a, Ord b) => Eq (VarBinding a b) where
        (==) = (==) `on` vbEnum

    -- | The Ord instance is defined only on the pairs of
    --   variables in the binding.
    instance (Ord a, Ord b) => Ord (VarBinding a b) where
        compare = comparing vbEnum

    -- | When combining instances, if there is an overlapping binding then
    --   the  value from the first instance is used.
    instance (Ord a, Ord b) => Monoid (VarBinding a b) where
        mempty = nullVarBinding
        mappend = joinVarBindings

    -- | The Show instance only displays the pairs of variables
    --    in the binding.
    --
    instance (Show a, Show b) => Show (VarBinding a b) where
        show = show . S.toList . vbEnum

    -- | The null, or empry, binding maps no query variables.
    --   This is the 'mempty' instance of the Monoid.
    --
    nullVarBinding :: VarBinding a b
    nullVarBinding = VarBinding
        { vbMap  = const Nothing
        , vbEnum = S.empty
        , vbNull = True
        }

    -- |Return a list of the variables bound by a supplied variable binding
    --
    boundVars :: (Ord a, Ord b) => VarBinding a b -> S.Set a
    boundVars = S.map fst . vbEnum  -- Ord b is needed got GHC 7.6

    -- |VarBinding subset function, tests to see if one query binding
    --  is a subset of another;  i.e. every query variable mapping defined
    --  by one is also defined by the other.
    --
    subBinding :: (Ord a, Ord b) => VarBinding a b -> VarBinding a b -> Bool
    subBinding = S.isSubsetOf `on` vbEnum

    -- |Function to make a variable binding from a list of
    --  pairs of variable and corresponding assigned value.
    --
    makeVarBinding :: (Ord a, Ord b) => [(a,b)] -> VarBinding a b
    makeVarBinding [] = nullVarBinding
    makeVarBinding vrbs =
        VarBinding
        { vbMap  = flip M.lookup (M.fromList vrbs)
        , vbEnum = S.fromList vrbs
        , vbNull = False
        }

    -- |Apply query binding to a supplied value, returning the value
    --  unchanged if no binding is defined
    --
    applyVarBinding :: VarBinding a a -> a -> a
    applyVarBinding vbind v = fromMaybe v (vbMap vbind v)

    -- |Join a pair of query bindings, returning a new binding that
    --  maps all variables recognized by either of the input bindings.
    --  If the bindings should overlap, such overlap is not detected and
    --  the value from the first binding provided is used.
    --
    joinVarBindings :: (Ord a, Ord b) => VarBinding a b -> VarBinding a b -> VarBinding a b
    joinVarBindings vb1 vb2
        | vbNull vb1 = vb2
        | vbNull vb2 = vb1
        | otherwise  = VarBinding
            { vbMap  = mv12
            , vbEnum = S.map (\v -> (v,fromJust (mv12 v))) bv12
            , vbNull = False
            }
        where
            mv12 n = vbMap vb1 n `mplus` vbMap vb2 n
            bv12 = boundVars vb1 `S.union` boundVars vb2

    -- |Add a single new value to a variable binding and return the resulting
    --  new variable binding.
    --
    addVarBinding ::
        (Ord a, Ord b)
        => a
        -> b
        -> VarBinding a b
        -> VarBinding a b
    addVarBinding lb val vbind = joinVarBindings vbind $ makeVarBinding [(lb,val)]

    ------------------------------------------------------------
    --  Datatypes for variable binding modifiers
    ------------------------------------------------------------

    -- |Define the type of a function to modify variable bindings in
    --  forward chaining based on rule antecedent matches.  This
    --  function is used to implement the \"allocated to\" logic described
    --  in Appendix B of the RDF semantics document, in which a specific
    --  blank node is associated with all matches of some specific value
    --  by applications of the rule on a given graph.
    --  Use 'id' if no modification of the variable bindings is required.
    --
    --  This datatype consists of the modifier function itself, which
    --  operates on a list of variable bindings rather than a single
    --  variable binding (because some modifications share context across
    --  a set of bindings), and some additional descriptive information
    --  that allows possible usage patterns to be analyzed.
    --
    --  Some usage patterns (see 'vbmUsage' for more details):
    --
    --  [filter]  all variables are input variables, and the effect
    --      of the modifier function is to drop variable bindings that
    --      don't satisfy some criterion.
    --      Identifiable by an empty element in @vbmUsage@.
    --
    --  [source]  all variables are output variables:  a raw query
    --      could be viewed as a source of variable bindings.
    --      Identifiable by an element of @vbmUsage@ equal to @vbmVocab@.
    --
    --  [modifier]  for each supplied variable binding, one or more
    --      new variable bindings may be created that contain the
    --      input variables bound as supplied plus some additional variables.
    --      Identifiable by an element of @vbmUsage@ some subset of @vbmVocab@.
    --
    --  A variety of variable usage patterns may be supported by a given
    --  modifier:  a modifier may be used to define new variable bindings
    --  from existing bindings in a number of ways, or simply to check that
    --  some required relationship between bindings is satisfied.
    --  (Example, for @a + b = c@, any one variable can be deduced from the
    --  other two, or all three may be supplied to check that the relationship
    --  does indeed hold.)
    --
    data VarBindingModify a b = VarBindingModify
        { vbmName   :: ScopedName
                                -- ^Name used to identify this variable binding
                                --  modifier when building inference rules.
        , vbmApply  :: [VarBinding a b] -> [VarBinding a b]
                                -- ^Apply variable binding modifier to a
                                --  list of variable bindings, returning a
                                --  new list.  The result list is not
                                --  necessarily the same length as the
                                --  supplied list.
        , vbmVocab  :: [a]      -- ^List of variables used by this modifier.
                                --  All results of applying this modifier contain
                                --  bindings for these variables.
        , vbmUsage  :: [[a]]    -- ^List of binding modifier usage patterns
                                --  supported.  Each pattern is characterized as
                                --  a list of variables for which new bindings
                                --  may be created by some application of this
                                --  modifier, assuming that bindings for all other
                                --  variables in @vbmVocab@ are supplied.
        }

    -- |Type for variable binding modifier that has yet to be instantiated
    --  with respect to the variables that it operates upon.
    --
    type OpenVarBindingModify lb vn = [lb] -> VarBindingModify lb vn

    -- |Extract variable binding name from @OpenVarBindingModify@ value
    --
    --  (Because only the name is required, the application to an undefined
    --  list of variable labels should never be evaluated, as long as the
    --  name is not dependent on the variable names in any way.)
    --
    --  NOT QUITE... some of the functions that create @OpenVarBindingModify@
    --  instances also pattern-match the number of labels provided, forcing
    --  evaluation of the labels parameter, even though it's not used.
    --
    openVbmName :: OpenVarBindingModify lb vn -> ScopedName
    openVbmName ovbm = vbmName (ovbm (error "Undefined labels in variable binding"))

    -- | Displays the name of the modifier.
    instance Show (OpenVarBindingModify a b)
        where
            show = show . openVbmName

    -- |Variable binding modifier compatibility test.
    --
    --  Given a list of bound variables and a variable binding modifier, return
    --  a list of new variables that may be bound, or @Nothing@.
    --
    --  Note:  if the usage pattern component is well-formed (i.e. all
    --  elements different) then at most one element can be compatible with
    --  a given input variable set.
    --
    vbmCompatibility :: (Eq a) => VarBindingModify a b -> [a] -> Maybe [a]
    vbmCompatibility vbm vars = find compat (vbmUsage vbm)
        where
            compat = vbmCompatibleVars vars (vbmVocab vbm)

    -- |Variable binding usage compatibility test.
    --
    --  Returns @True@ if the supplied variable bindings can be compatibly
    --  processed by a variable binding usage with supplied vocabulary and
    --  usage pattern.
    --
    vbmCompatibleVars ::
      (Eq a)
      => [a] -- ^ variables supplied with bindings
      -> [a] -- ^ variables returned with bindings by a modifier
      -> [a] -- ^ variables assigned new bindings by a modifier
      -> Bool
    vbmCompatibleVars bvars vocab ovars =
        null (ivars `intersect` ovars) &&       -- ivars and ovars don't overlap
        null ((vocab \\ ovars) \\ ivars)        -- ovars and ivars cover vocab
        where
            ivars = bvars `intersect` vocab

    -- |Compose variable binding modifiers.
    --
    --  Returns @Just a@ new variable binding modifier that corresponds to
    --  applying the first supplied modifier and then applying the second
    --  one, or @Nothing@ if the two modifiers cannot be compatibly composed.
    --
    --  NOTE:  this function does not, in general, commute.
    --
    --  NOTE:  if there are different ways to achieve the same usage, that
    --  usage is currently repeated in the result returned.
    --
    vbmCompose :: (Eq a) => VarBindingModify a b -> VarBindingModify a b
        -> Maybe (VarBindingModify a b)
    vbmCompose
        (VarBindingModify nam1 app1 voc1 use1)
        (VarBindingModify nam2 app2 voc2 use2)
        | not (null use12) = Just VarBindingModify
            { vbmName  = name
            , vbmApply = app2 . app1
            , vbmVocab = voc1 `union` voc2
            , vbmUsage = use12
            }
        | otherwise = Nothing
        where
            use12 = compatibleUsage voc1 use1 use2
            getName = getLName . getScopeLocal
            -- since _ is a valid LName component then we know the mconcat output
            -- is a valid LName and so can use fromJust
            name = swishName $ fromJust $ newLName $ mconcat ["_", getName nam1, "_", getName nam2, "_"]

    -- |Determine compatible ways in which variable binding modifiers may
    --  be combined.
    --
    --  The total vocabulary of a modifier is the complete set of variables
    --  that are used or bound by the modifier.  After the modifier has been
    --  applied, bindings must exist for all of these variables.
    --
    --  A usage pattern of a modifier is a set of variables for which new
    --  bindings may be generated by the modifier.
    --
    --  The only way in which two variable binding modifiers can be incompatible
    --  with each other is when they both attempt to create a new binding for
    --  the same variable.  (Note that this does not mean the composition will
    --  be compatible with all inputs:  see @vbmCompatibleVars@.)
    --
    --  NOTE:  if there are different ways to achieve the same usage, that
    --  usage is currently repeated in the result returned.
    --
    compatibleUsage ::
      (Eq a)
      => [a]   -- ^ the total vocabulary of the first modifier to be applied
      -> [[a]] -- ^ usage patterns for the first modifier
      -> [[a]] -- ^ usage patterns for the second modifier
      -> [[a]] -- ^ a list of possible usage patterns for the composition of
               --  the first modifier with the second modifier, or an empty list if
               --  the modifiers are incompatible.
    compatibleUsage voc1 use1 use2 =
        [ u1++u2 | u2 <- use2, null (voc1 `intersect` u2), u1 <- use1 ]

    -- |Find all compatible compositions of a list of variable binding
    --  modifiers for a given set of supplied bound variables.
    findCompositions ::
        (Eq a) => [VarBindingModify a b]
        -> [a]
        -> [VarBindingModify a b]
    findCompositions vbms vars =
        mapMaybe (composeCheckSequence vars) (permutations vbms)

    -- |Compose sequence of variable binding modifiers, and check
    --  that the result can be used compatibly with a supplied list
    --  of bound variables, returning @Just (composed modifier)@,
    --  or @Nothing@.
    --
    composeCheckSequence :: (Eq a) => [a] -> [VarBindingModify a b]
        -> Maybe (VarBindingModify a b)
    composeCheckSequence vars vbms = useWith vars $ composeSequence vbms
        where
            --  Check that a Maybe modifier is compatible for use with an
            --  indicated set of bound variables, and return (Just modifier)
            --  or Nothing.
            useWith _    Nothing    = Nothing
            useWith vs v@(Just vbm)
                | isJust $ vbmCompatibility vbm vs = v
                | otherwise                        = Nothing

    -- |Compose sequence of variable binding modifiers.
    --
    composeSequence :: (Eq a) => [VarBindingModify a b]
        -> Maybe (VarBindingModify a b)
    composeSequence [] = Just varBindingId
    composeSequence (vbm:vbms) = foldl' composePair (Just vbm) vbms

    -- |Compose a pair of variable binding modifiers, returning
    --  @Just (composed modifier)@, or @Nothing@.
    --
    composePair :: (Eq a) => Maybe (VarBindingModify a b) -> VarBindingModify a b
        -> Maybe (VarBindingModify a b)
    composePair Nothing     _    = Nothing
    composePair (Just vbm1) vbm2 = vbmCompose vbm1 vbm2

    -- |Return @Just a@ compatible composition of variable binding modifiers
    --  for a given set of supplied bound variables, or @Nothing@ if there
    --  is no compatible composition
    --
    findComposition :: (Eq a) => [VarBindingModify a b] -> [a]
        -> Maybe (VarBindingModify a b)
    findComposition = listToMaybe `c2` findCompositions
        where
            c2 = (.) . (.)  -- compose with function of two arguments

    -- |Variable binding modifier that returns exactly those
    --  variable bindings presented.
    --
    varBindingId :: VarBindingModify a b
    varBindingId = VarBindingModify
        { vbmName   = swishName "varBindingId"
        , vbmApply  = id
        , vbmVocab  = []
        , vbmUsage  = [[]]
        }

    -- |Null variable binding modifier
    --
    --  This is like 'varBindingId' except parameterized by some labels.
    --  I think this is redundant, and should be eliminated.
    --
    nullVarBindingModify :: OpenVarBindingModify a b
    nullVarBindingModify lbs = VarBindingModify
        { vbmName   = swishName "nullVarBindingModify"
        , vbmApply  = id
        , vbmVocab  = lbs
        , vbmUsage  = [[]]
        }

    ------------------------------------------------------------
    --  Query binding filters
    ------------------------------------------------------------

    -- |VarBindingFilter is a function type that tests to see if
    --  a query binding satisfies some criterion.
    --
    --  Queries often want to apply some kind of filter or condition
    --  to the variable bindings that are processed.  In inference rules,
    --  it sometimes seems desirable to stipulate additional conditions on
    --  the things that are matched.
    --
    --  This function type is used to perform such tests.
    --  A number of simple implementations are included below.
    data VarBindingFilter a b = VarBindingFilter
        { vbfName   :: ScopedName
        , vbfVocab  :: [a]
        , vbfTest   :: VarBinding a b -> Bool
        }

    -- |Make a variable binding modifier from a variable binding filter value.
    makeVarFilterModify :: VarBindingFilter a b -> VarBindingModify a b
    makeVarFilterModify vbf = VarBindingModify
        { vbmName   = vbfName vbf
        , vbmApply  = filter (vbfTest vbf)
        , vbmVocab  = vbfVocab vbf
        , vbmUsage  = [[]]
        }

    -- |Make a variable test filter for a named variable using a
    --  supplied value testing function.
    makeVarTestFilter ::
        ScopedName -> (b -> Bool) -> a -> VarBindingFilter a b
    makeVarTestFilter nam vtest var = VarBindingFilter
        { vbfName   = nam
        , vbfVocab  = [var]
        , vbfTest   = \vb -> maybe False vtest (vbMap vb var)
        }

    -- |Make a variable comparison filter for named variables using
    --  a supplied value comparison function.
    makeVarCompareFilter ::
        ScopedName -> (b -> b -> Bool) -> a -> a -> VarBindingFilter a b
    makeVarCompareFilter nam vcomp v1 v2 = VarBindingFilter
        { vbfName   = nam
        , vbfVocab  = [v1,v2]
        , vbfTest   = \vb -> fromMaybe False (vcomp <$> vbMap vb v1 <*> vbMap vb v2)
        }

    ------------------------------------------------------------
    --  Declare some generally useful query binding filters
    ------------------------------------------------------------

    -- |This function generates a query binding filter that ensures that
    --  two indicated query variables are mapped to the same value.
    varFilterEQ :: (Eq b) => a -> a -> VarBindingFilter a b
    varFilterEQ =
        makeVarCompareFilter (swishName "varFilterEQ") (==)

    -- |This function generates a query binding filter that ensures that
    --  two indicated query variables are mapped to different values.
    varFilterNE :: (Eq b) => a -> a -> VarBindingFilter a b
    varFilterNE =
        makeVarCompareFilter (swishName "varFilterNE") (/=)

    -- |This function composes a number of query binding filters
    --  into a composite filter that accepts any query binding that
    --  satisfies at least one of the component values.
    varFilterDisjunction :: (Eq a) => [VarBindingFilter a b]
        -> VarBindingFilter a b
    varFilterDisjunction vbfs = VarBindingFilter
        { vbfName   = swishName "varFilterDisjunction"
        , vbfVocab  = foldl1 union (map vbfVocab vbfs)
        , vbfTest   = or . flist (map vbfTest vbfs)
        }

    -- |This function composes a number of query binding filters
    --  into a composite filter that accepts any query binding that
    --  satisfies all of the component values.
    --
    --  The same function could be achieved by composing the component
    --  filter-based modifiers, but this function is more convenient
    --  as it avoids the need to check for modifier compatibility.
    --
    varFilterConjunction :: (Eq a) => [VarBindingFilter a b]
        -> VarBindingFilter a b
    varFilterConjunction vbfs = VarBindingFilter
        { vbfName   = swishName "varFilterConjunction"
        , vbfVocab  = foldl1 union (map vbfVocab vbfs)
        , vbfTest   = and . flist (map vbfTest vbfs)
        }

    --------------------------------------------------------------------------------
    --
    --  (c) 2003, Graham Klyne, 2009 Vasili I Galchin,
    --    2011, 2012 Douglas Burke
    --  All rights reserved.
    --
    --  This file is part of Swish.
    --
    --  Swish is free software; you can redistribute it and/or modify
    --  it under the terms of the GNU General Public License as published by
    --  the Free Software Foundation; either version 2 of the License, or
    --  (at your option) any later version.
    --
    --  Swish is distributed in the hope that it will be useful,
    --  but WITHOUT ANY WARRANTY; without even the implied warranty of
    --  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    --  GNU General Public License for more details.
    --
    --  You should have received a copy of the GNU General Public License
    --  along with Swish; if not, write to:
    --    The Free Software Foundation, Inc.,
    --    59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
    --
    --------------------------------------------------------------------------------